Digital to analog (D/A) converters can include arrays of capacitors that are selectively switched to convert a digital signal to an analog counterpart. However, mismatch between capacitors may cause the D/A converter to be non-monotonic. Monotonicity in a D/A converter means that as the digital input to the converter increases over a full-scale range, the analog output never exhibits a decrease between one conversion step and a subsequent conversion step. In other words, the slope of the transfer characteristic is never negative in a monotonic converter.
Referring now to FIG. 1A, a D/A converter 10 is shown. The D/A converter 10 includes a binary capacitor array 14, switches 16 and 18, an operational amplifier (opamp) 20, and a capacitor Cf in a feedback arrangement with the opamp 20. Each of the capacitors in the array 14 have different values. More particularly, each capacitor in the array 14 is twice the value of the preceding capacitor. Switches SW selectively switch the capacitors in the array 14 between a voltage reference and a reference potential such as ground.
In use, the D/A converter 10 has sampling and integration stages. In the sampling stage, the switch 16 closes and selective ones of the capacitors are charged to the voltage reference as determined by the switches. In the integrating phase, the switch 16 is opened and the analog output is generated. For example, a four bit array may close a first or most significant bit (MSB) switch and a least significant bit (LSB) switch to represent 9/16 of a voltage reference.
Referring now to FIG. 1B, a non-monotonic output of a D/A converter is shown. For example, the analog output exhibits a decrease from one conversion step to the subsequent conversion step as shown at in FIG. 1B at 44. The non-monotonic output may be due to capacitor mismatch. For example, the capacitor 2N−1C may be different than 2N−2C+2N−3C+ . . . +2C+C. Ideally, 2N−1C−(2N−2C+2N−3C+ . . . +2C+C)=C. In other words, the difference between the MSB capacitor and the rest of the capacitors should be equal to a smallest or LSB capacitor
Referring now to FIG. 2, a D/A converter 50 including a linear capacitor array 54 is shown. The linear capacitor array 54 includes 2N−1 capacitors that are selectively switched between a voltage reference and reference potential such as ground. While the linear capacitor array 54 inherently monotonic, the number of switches required grows exponentially with the bit resolution. For example, a 16-bit digital to analog converter includes 216−1 pairs of switches, which may be impractical.